Rational Numbers (Class 8)

What this worksheet covers

This is an eighteen-question practice worksheet on rational numbers for Class 8, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on rational numbers at Class 8 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Rough work may be done on the blank space at the side of each page.

Sample questions from this worksheet

A preview of what's inside Rational Numbers (Class 8) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. The additive inverse of {−5/7} is _______.

   • A{5/7}correct
   • B{−7/5}
   • C{7/5}
   • D0
   Solution: The additive inverse of a number is what must be added to it to give 0. Since {−5/7} + {5/7} = 0, the additive inverse is {5/7}.

2. 2. Which of the following rational numbers lies between {1/3} and {1/2}?

   • A{1/4}
   • B{2/3}
   • C{5/12}correct
   • D{7/12}
   Solution: Write both numbers with denominator 12: {1/3} = {4/12} and {1/2} = {6/12}. The only option lying strictly between {4/12} and {6/12} is {5/12}. Checking the others: {1/4} = {3/12} is too small, while {2/3} = {8/12} and {7/12} are too large.

3. 3. Consider the following statements.(i) Every integer is a rational number.(ii) Every rational number is an integer.(iii) 0 has no reciprocal.Which of the statements is/are correct?

   • A(i) and (ii) only
   • B(i) and (iii) onlycorrect
   • C(ii) and (iii) only
   • DAll three
   Solution: Statement (i) is true — any integer n can be written as {n/1}. Statement (ii) is false; {1/2} is a rational number but not an integer. Statement (iii) is true; the reciprocal of 0 would have to be {1/0}, which is not defined. Hence (i) and (iii).